The server and desktop are basically the same thing but server does not have GUI stuff (xorg, desktop manager and …) installed. On the same time server might have packages installed that would not be there if use Ubuntu on a desktop.
Before you start, it is always good to update packages list before you install something:
sudo apt-get update
The easiest solution would be to use a program called Tasksel that you can install by typing:
sudo apt-get install tasksel
Run it by typing:
sudo tasksel
It gives you a simple gui to manage larger software bundles (“LAMP server”, “Ubuntu desktop”, “Lubuntu desktop”) that have been installed in your system. Mark the stuff you need with asterisks by selecting them with up/down arrows and pressing space. After that press enter install what you have selected. To install regular Ubuntu desktop choose “Ubuntu desktop”.
If the Tasksel does not work for some reason. You can install packages that come with the regular Desktop installation (Unity) with this:
sudo apt-get install ubuntu-desktop
If you prefer Lubuntu flavour use the lubuntu-desktop package or if you prefer KDE use the kubuntu-desktop package or if you want Xfce use the xubuntu-desktop package instead of ubuntu-desktop.